Base field: \(\Q(\sqrt{-26}) \)
Generator \(a\), with minimal polynomial \(x^2 + 26\); class number \(6\).
Form
| Weight: | 2 | |
| Level: | 637.2 = \( \left(91, 7 a\right) \) | |
| Level norm: | 637 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 5824.2.a.f , 1183.2.a.a |
| Newspace: | 2.0.104.1-637.2 (dimension 14) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.104.1-637.2-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 7 \) | 7.1 = \( \left(7, a + 3\right) \) | \( 1 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( 1 \) |
| \( 13 \) | 13.1 = \( \left(13, a\right) \) | \( 1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 26 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -2 \) |
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 0 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 0 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( -3 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( -3 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 5\right) \) | \( 4 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 12\right) \) | \( 4 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 6\right) \) | \( -3 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 25\right) \) | \( -3 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 14\right) \) | \( -4 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 23\right) \) | \( -4 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 19\right) \) | \( -1 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 24\right) \) | \( -1 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 16\right) \) | \( 7 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 31\right) \) | \( 7 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 20\right) \) | \( -8 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 51\right) \) | \( -8 \) |
| \( 107 \) | 107.1 = \( \left(a + 9\right) \) | \( -4 \) |
| \( 107 \) | 107.2 = \( \left(a - 9\right) \) | \( -4 \) |
| \( 109 \) | 109.1 = \( \left(109, a + 44\right) \) | \( -2 \) |